a Examining the diagram, we can identify three given pieces of information.
B
b The sides with an equal number of hatch marks are congruent.
A
a See solution.
B
b See solution.
Practice makes perfect
a Let's mark the given information in the diagram.
To prove that the acute angles of a right triangle are complementary, we only need information about the angles. Therefore, we can disregard the given information about the segments.
Given: &∠ M is a right angle
Prove: &The acute angles of a right
&triangle are complementary.
b From Part A, we know three given statements about the triangle.
MN≅ NJ
JK≅ KL
∠ M is a right angle.
To prove statements about the sides of the triangle, we can disregard the information about the angle. Therefore, we can write a given and prove statement for the conclusion in Part B.
Given: &MN≅ NJ and JK≅ KL
Prove: &The segment connecting the
&midpoints of two sides of a
&triangle is half as long as
&the third side
